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**Global stability and predator dynamics in a model of prey dispersal in a patchy environment.**
*(English)*
Zbl 0685.92018

A model of a single species dispersing among n patches of a heterogeneous environment with barriers between patches and with a predator for which the barriers are not an obstacle, is described. The model is a system of autonomous ODEs. It is shown to possess positive equilibria for the prey (with a null state of the predator) if some relations between the barrier strength and the growth rates of the prey in the patches are fulfilled. The equilibria are globally stable in the absence of a predator. The question of persistence of the predator is also considered.

Reviewer: T.V.Kostova-Vassilevska

### MSC:

92D40 | Ecology |

92D25 | Population dynamics (general) |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

### Keywords:

predator-prey; patchy environment; dispersal; global asymptotic; stability; extinction; heterogeneous environment; barriers between patches; positive equilibria; persistence
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\textit{H. I. Freedman} and \textit{Y. Takeuchi}, Nonlinear Anal., Theory Methods Appl. 13, No. 8, 993--1002 (1989; Zbl 0685.92018)

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### References:

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